Добавил шестую лабу

3 files changed, 236 insertions, 0 deletions

diff --git a/lab6/Cargo.lock b/lab6/Cargo.lock
new file mode 100644
index 0000000..1281335
--- /dev/null
+++ b/lab6/Cargo.lock
@@ -0,0 +1,65 @@
+# This file is automatically @generated by Cargo.
+# It is not intended for manual editing.
+version = 3
+
+[[package]]
+name = "az"
+version = "1.2.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "7b7e4c2464d97fe331d41de9d5db0def0a96f4d823b8b32a2efd503578988973"
+
+[[package]]
+name = "gmp-mpfr-sys"
+version = "1.4.10"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "ea3f42dadb6c75f122e9aa87e757ef11d4282f664c9f2e6476a9c2c8970f9d19"
+dependencies = [
+ "libc",
+ "winapi",
+]
+
+[[package]]
+name = "lab1"
+version = "0.1.0"
+dependencies = [
+ "rug",
+]
+
+[[package]]
+name = "libc"
+version = "0.2.134"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "329c933548736bc49fd575ee68c89e8be4d260064184389a5b77517cddd99ffb"
+
+[[package]]
+name = "rug"
+version = "1.17.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "203180f444c95eac53586ed04793ecf6454c5d28f9eca8eead815fc19e136c47"
+dependencies = [
+ "az",
+ "gmp-mpfr-sys",
+ "libc",
+]
+
+[[package]]
+name = "winapi"
+version = "0.3.9"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "5c839a674fcd7a98952e593242ea400abe93992746761e38641405d28b00f419"
+dependencies = [
+ "winapi-i686-pc-windows-gnu",
+ "winapi-x86_64-pc-windows-gnu",
+]
+
+[[package]]
+name = "winapi-i686-pc-windows-gnu"
+version = "0.4.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "ac3b87c63620426dd9b991e5ce0329eff545bccbbb34f3be09ff6fb6ab51b7b6"
+
+[[package]]
+name = "winapi-x86_64-pc-windows-gnu"
+version = "0.4.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "712e227841d057c1ee1cd2fb22fa7e5a5461ae8e48fa2ca79ec42cfc1931183f"
diff --git a/lab6/Cargo.toml b/lab6/Cargo.toml
new file mode 100644
index 0000000..1370852
--- /dev/null
+++ b/lab6/Cargo.toml
@@ -0,0 +1,9 @@
+[package]
+name = "lab1"
+version = "0.1.0"
+edition = "2021"
+
+# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
+
+[dependencies]
+rug = "1.17"
diff --git a/lab6/src/main.rs b/lab6/src/main.rs
new file mode 100644
index 0000000..e066fe4
--- /dev/null
+++ b/lab6/src/main.rs
@@ -0,0 +1,162 @@
+use rug::{Complete, Integer, rand::RandState};
+use std::io;
+
+fn solovey_strassen_test(n: &Integer, k: u32) -> bool {
+    let mut rand = RandState::new();
+    for _ in 0..k {
+        let bound = n.clone() - 3u32;
+        let a = bound.random_below(&mut rand) + 2u32;
+
+        let gcd = a.gcd_ref(n).complete();
+        if gcd > 1 {
+            return false;
+        }
+
+        let x1 = legendre(&a, n);
+        let x2 = jacobi(&a, n);
+        if x1 != x2 {
+            return false;
+        }
+    }
+    return true;
+}
+
+fn jacobi(a: &Integer, p: &Integer) -> Integer {
+    let factors = factorize(&p);
+    let mut result = Integer::from(1u32);
+    for factor in &factors {
+        let x = legendre(a, &factor);
+        result *= x;
+    }
+    return result;
+}
+
+fn legendre(a: &Integer, p: &Integer) -> Integer {
+    let power = (p.clone() - 1u32)
+                .div_exact_ref(&Integer::from(2u32))
+                .complete();
+    let result = Integer::from(a.pow_mod_ref(&power, &p).unwrap());
+    if result == 0 || result == 1 {
+        result
+    }
+    else {
+        Integer::from(-1)
+    }
+}
+
+fn main() {
+    println!("Введите положительное нечётное число n:");
+    let mut p = String::new();
+    let stdin = io::stdin();
+    match stdin.read_line(&mut p) {
+        Ok(_) => (),
+        Err(_) => {
+            println!("Произошла ошибка при чтении из стандартного ввода");
+            return ();
+        }
+    }
+    let p = match Integer::parse(p) {
+        Ok(parsed) => parsed.complete(),
+        Err(_) => {
+            println!("Не удалось считать число");
+            return ();
+        }
+    };
+    if p.is_divisible(&Integer::from(2u32)) {
+        println!("Введено чётное число");
+        return ();
+    }
+
+    println!("Введите количество раундов k:");
+    let mut k = String::new();
+    match stdin.read_line(&mut k) {
+        Ok(_) => (),
+        Err(_) => {
+            println!("Произошла ошибка при чтении из стандартного ввода");
+            return ();
+        }
+    }
+    let k = match k.trim_end().parse::<u32>() {
+        Ok(parsed) => parsed,
+        Err(_) => {
+            println!("Не удалось считать число");
+            return ();
+        }
+    };
+
+    let is_prime = solovey_strassen_test(&p, k);
+    if is_prime {
+        let probability = 1f64 - 2f64.powf(-(k as f64));
+        println!("Число {} является простым с вероятностью {}", &p, probability);
+    }
+    else {
+        println!("Число не является простым");
+    }
+}
+
+fn factorize(n: &Integer) -> Vec<Integer> {
+    let mut factors = Vec::new();
+    let mut front = vec![n.clone()];
+
+    while !front.is_empty() {
+        let num = front.pop().unwrap();
+        match lehman(&num) {
+            Some(factor) => {
+                let other = num.div_exact_ref(&factor).complete();
+                front.push(factor);
+                front.push(other);
+            },
+            None => factors.push(num)
+        };
+    }
+
+    return factors;
+}
+
+fn lehman(n: &Integer) -> Option<Integer> {
+    let one = &Integer::from(1u32);
+    let mut a = Integer::from(2u32);
+    let root3 = n.root_ref(3).complete();
+
+    while a <= root3 {
+        let (_, r) = n.div_rem_ref(&a).complete();
+        if r == 0 {
+            return Some(a);
+        }
+        a += one;
+    }
+
+    let root6 = n.root_ref(6).complete();
+    let mut k = Integer::from(1u32);
+    while k <= root3 {
+        let mut d = Integer::ZERO;
+        let sqrtk4 = k.sqrt_ref().complete() * 4;
+        let (r6sk4, _) = root6.div_rem_ref(&sqrtk4).complete();
+        while d <= (&r6sk4 + one).complete() {
+            let kn4: Integer = k.clone() * n.clone() * 4;
+            let sqrt_kn4 = kn4.sqrt_ref().complete();
+
+            let number = (sqrt_kn4.clone() + d.clone()).square() - kn4.clone();
+            if number.is_perfect_square() {
+                let big_a = sqrt_kn4 + d.clone();
+                let big_b = (big_a.square_ref() - kn4).sqrt();
+
+                let gcd1 = (big_a.clone() + big_b.clone()).gcd_ref(n).complete();
+                let gcd2 = (big_a.clone() - big_b.clone()).gcd_ref(n).complete();
+
+                if &gcd1 > one && &gcd1 < n {
+                    return Some(gcd1);
+                }
+                else if &gcd2 > one && &gcd2 < n {
+                    return Some(gcd2);
+                }
+            }
+
+            d += one;
+        }
+        k += one;
+    }
+
+    return None;
+}
+